sound Longitudinal waves that propagate through matter by transfer of kinetic energy from one molecule to another. Intermolecular collisions transfer the energy in gases. In solids and liquids intermolecular forces and collisions are responsible for the transfer of energy. Velocity of sound is greater in solids and liquids than in gases. The velocity of sound in gas is slightly less than the root mean square velocity * of the molecules in the gas. The sound velocity increases with increasing temperature since it gives larger molecular velocity. In a solid the velocity of sound is given by,

v = (E/r )^1/2 (s8)

where E is the Young modulus and r is the density of the material.

For a gas,

v=(g P/r ) ^1/2 (s9)

where g is the ratio of specific heats at constant pressure and constant volume, P the pressure and r the density. Since PV=RT,

v = (g RT/M) ^1/2 (s10)

where M is the molar mass of the gas. It shows that the velocity of sound is independent of the gas pressure.

For a liquid the expression for velocity is the same as that for a solid, Eq(s8), only the elastic constant is replaced by the bulk modulus B of the liquid.

v=(B/r )^1/2 (s11)

For sound waves in air the pressure fluctuations are ~ 1 Pa whereas the atmospheric pressure is ~ 10⁵ Pa.

The vibration of fluid particles when sound is propagating through it may also be described in terms of variation of pressure at the same point. The pressure fluctuates about the normal pressure with same frequency as that of displacement.

For a simple harmonic wave the displacement is given by,

y = a sin (w t - kx) (s13)

while the equation of pressure is,

p = - p₀ cos (w t - kx) (s14)

where p₀ = w r va

is the pressure wave amplitude. Comparing equations (s13) and (s14) we observe that displacement and pressure are 90^o out of phase.

The intensity of sound wave, I is power carried by the wave through unit area held normally to the direction of propagation of the wave.

I = 2p ²n ²r va² = p₀²/2r v (s15)

Sound waves beyond the frequency 20 000Hz are called ultrasonic waves *. We cannot hear ultrasonic waves although some animals are capable of hearing it.

There are three properties that characterize our perception of sound. These are loudness, pitch and quality. The loudness as perceived by us is approximately proportional to logarithm of intensity. The scale of loudness is decibel . The pitch is frequency of vibration of the source.